Final answer:
Chance causes refer to natural and random variations in a process, while assignable causes are identifiable variations that can be addressed. In a Shewhart control chart, these variability causes are critical for understanding whether a process is in control or if there's an issue that requires attention.
Step-by-step explanation:
Chance causes and assignable causes are two types of sources of variability in processes, especially in the context of quality control.
Chance causes, also known as common causes, refer to the natural and random variations that occur in a process when it is operating under control. These could include slight variations in temperature, humidity, or material quality, which are expected as part of the normal process operation and are usually acceptable within certain limits.
Assignable causes, in contrast, are sources of variation that can be identified and eliminated. These are unexpected issues that arise and are not part of the natural variability of the process. Examples include machine malfunction, human error, or a sudden change in material quality.
In the operation and interpretation of a Shewhart control chart, which is a tool used in statistical process control, these causes of variability play a critical role. The control chart is designed to help distinguish between these two types of variability. If a point falls within the control limits, it is considered to be the result of chance causes. However, if a point falls outside these limits, it suggests an assignable cause that may require investigation and corrective action.